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Finance and Stochastics

14.06.2021

Duality theory for robust utility maximisation

verfasst von: Daniel Bartl, Michael Kupper, Ariel Neufeld

Erschienen in: Finance and Stochastics | Ausgabe 3/2021

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Abstract

In this paper, we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real line. Our results are inspired by – and can be seen as the robust analogues of – the seminal work of Kramkov and Schachermayer (Ann. Appl. Probab. 9:904–950, 1999). Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximisation problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty.

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Metadaten
Titel
Duality theory for robust utility maximisation
verfasst von
Daniel Bartl
Michael Kupper
Ariel Neufeld
Publikationsdatum
14.06.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Finance and Stochastics / Ausgabe 3/2021
Print ISSN: 0949-2984
Elektronische ISSN: 1432-1122
DOI
https://doi.org/10.1007/s00780-021-00455-6